In this paper we present an exact study of the relaxation dynamics of the back-gammon model. This is a model of a gas of particles in a discrete space which presents glassy phenomena as a result of entropr barriers in configuration space. The model is simple enough to allow Ibr a complete analytical treatment of the dynamics in infinite dimensions. We first derive a closed equation describing the evolution of the occupation number probabilities, then we generalize the analysis to the study the autocorrelation function. We also consider possible variants of the model which allow us to study the effect of energy barriers.